Focal length of concave lens using convex lens

[Amith2006]

# A convex lens of focal length 10 cm forms a real image of an object placed at a distance of 20 cm from it. Midway between the convex lens and the position of the image a thin concave lens is introduced. The image formed now is at a distance of 5 cm away from the earlier position. What is the focal length of the concave lens?
I solved it in the following way:
Case-1
Let u, v and f be the object distance, image distance and the focal length of the convex lens.
Here u = 20 cm, f = + 10 cm
1/v = 1/f – 1/u
1/v= 1/10 – 1/20
v = 20 cm
Case- 2
Let u, v and f be the object distance, image distance and the focal length of the concave lens.
Here u = - 10(virtual object), v = + 15 cm
1/f = -1/10 + 1/15
f = - 30 cm
But the answer given in my book is – 5 cm.

 

[Gokul43201]

I don't get 5 cm either.

But I think you made a mistake with setting v=15cm in the second part. Would you expect the image for a concave lens to be 5cm closer to the lens or 5cm farther from it (compared to the object)?

 

[Amith2006]

I assumed it to be away because i felt that concave lens is diverging in nature and so the image would be produced 5 cm away from the lens. What do you say?

 

[Gokul43201]

That sounds right (that the image would be farther away). There must be a mistake with the way I was doing it. I'm too sleepy to think straight now. I'll look at this again when I find some free time. Meanwhile someone else might have something useful to say.